He insisted Romney was "hiding something" by refusing to release more tax returns.
Reid, D-Nev., started the day on the Senate floor alleging the multimillionaire presumptive Republican presidential nominee paid no federal income taxes for 10 years -- an allegation he has made for several days but not on the Senate floor until Thursday.
Reid did not substantiate the allegation, other than to attribute it to a Bain Capital investor and others who he said were "extremely credible."
Romney responded, telling talk show host Sean Hannity Reid better offer proof to support his tax claims or stop making them.
"It's time for Harry to put up or shut up," he said.
"Harry's going to have to describe who it is he spoke with because of course that's totally and completely wrong," he said. "It's untrue, dishonest and inaccurate. It's wrong. So I'm looking forward to have Harry reveal his sources, and we'll probably find out it's the White House."
Romney has not released his income-tax returns from before 2010, leading Democrats to speculate they contain embarrassments.
A recent campaign ad for President Barack Obama said the former Massachusetts governor's secrecy on the issue "makes you wonder if some years he paid any taxes at all."
The Obama campaign has not said anything in support of Reid's specific allegation.
Reid responded to Romney's radio comments Thursday night, repeating he "was told by an extremely credible source that Romney has not paid taxes for 10 years.
"People who make as much money as Mitt Romney have many tricks at their disposal to avoid paying taxes," Reid's statement said. "We already know that Romney has exploited many of these loopholes, stashing his money in secret, overseas accounts in places like Switzerland and the Cayman Islands."
Reid revived a criticism that Romney did not follow through on a promise he made to ABC News last week that he would be "happy to go back" and check his tax returns and to see if he ever paid an effective tax rate below the 13.9 percent rate he paid in 2010, the only year's complete tax return he has released.
A day later his campaign said Romney had no intention of putting out any further information. The campaign has declined to answer further questions on the matter.
"When it comes to answering the legitimate questions the American people have about whether he avoided paying his fair share in taxes or why he opened a Swiss bank account, Romney has shut up," Reid said.
"But as a presidential candidate, it's his obligation to put up, and release several years' worth of tax returns just like nominees of both parties have done for decades.
"It's clear Romney is hiding something, and the American people deserve to know what it is," Reid said.
"Whatever Romney's hiding probably speaks volumes about how he would approach issues that directly impact middle-class families, like tax reform and the economy. When you are running for president, you should be an open book," he said.
A second source close to Reid told CNN the original source for Reid's claim was a Bain investor and a "credible person."
Another source who claims to know the Bain investor told The Huffington Post that "if we knew the name we would understand they would have the authority and the ability to know about Romney's tax returns," the Post reported.
Romney's campaign had no immediate comment on Reid's latest statement.